Match Equivalent Expressions: 3(y+b)+4x and Related Forms

To solve this problem, we'll follow these steps:

• Step 1: Expand each of the given expressions using the distributive property.
• Step 2: Simplify the resulting expressions.
• Step 3: Match the simplified expressions with options a, b, and c.

Now, let's work through each step:
Step 1: Start with the first expression $3(y+b) + 4x$.
Applying the distributive property: $3 \cdot y + 3 \cdot b + 4x = 3y + 3b + 4x$. This matches with option a: $3y+3b+4x$.

Step 2: Consider the second expression $(3+4x)(y+b)$.
Expanding using the distributive property, we get: $3(y+b) + 4x(y+b) = 3y + 3b + 4xy + 4xb$. This matches with option c: $3y+3b+4xy+4xb$.

Step 3: Finally, expand the third expression $(4y+3)(x+b)$.
Apply the distributive property: $4y(x+b) + 3(x+b) = 4yx + 4yb + 3x + 3b$. This matches with option b: $4yx+4yb+3x+3b$.

Therefore, the matches are:
First expression matches option a
Second expression matches option c
Third expression matches option b

Therefore, the solution to the problem is 1-a, 2-c, 3-b.